## The AIM@SHAPE Glossary

### Alphabetical list of terms

- parabolic line
- A parabolic line on a surface consists of points where one of the principal curvature vanishes.
- parametric continuity
- Two Ck function pieces join smoothly at a boundary to form a joint Ck function if, at all common points, their kth derivatives agree for k = 0,1,2, ,k. For k=0, it is a point continuity, for k=1, it is a continuity of first derivative, for k=2, it is a continuity of second derivative. It cannot be inferred that curve or surface pieces join smoothly if the derivatives of the component functions agree.
- parametric curve/surface
- Any curve/surface defined on a parametric domain. In case of surfaces, such domain can be usually tensor-based or triangular. Bezier, B-Splines, NURBS curves/surfaces belong to this category.
- parametric modelling
- Method of supporting the generation of model variations in CAD systems, storing an object as a main shape description and parameters for the dimensions and/or topology. After the assignment of specific values to the parameters, the modelling system generates a model variant accordingly.
- parametric surface
- A function with domain R2 and range R3.
- pca
- See Principal Component Analysis.
- pivot
- The pivot makes the flexion axis rotate around the limb which is influenced by the joint.
- pixel
- A picture element, one or more measurements at a particular integer coordinate of a 2-D image.
- point cloud
- A set of uncorrelated points, usually in 3D, which have to be further elaborated to obtain a 3D model.
- point set
- See Point Cloud.
- polyhedral terrain
- A polyhedral terrain is the image of a piecewise-linear function f. The most commonly used polyhedral terrain models are triangulated irregular networks (TINs), in which the domain partition forms a triangle mesh.
- post-processing
- In a FE context, phase of the finite element analysis in which the analyst checks the validity of the solution, examines the values of primary quantities (such as displacements and stresses), and derives and examines additional quantities (such as specialized stresses and error indicators).
- pre-processing
- In a FE context, phase of the finite element analysis where the analyst develops a finite element mesh to divide the subject geometry into sub domains for mathematical analysis, and applies material properties and boundary conditions.
- principal component analysis
- A technique that can be used to simplify a dataset; more formally it is a linear transformation that chooses a new coordinate system for the data set such that the greatest variance by any projection of the data set comes to lie on the first axis (then called the first principal component), the second greatest variance on the second axis, and so on. ...
- principal curvatures
- The maximum and minimum of the normal curvature k1 and k2 at a given point on a surface are called the principal curvatures. The principal curvatures measure the maximum and minimum bending of a regular surface at each point.
- product development process
- A disciplined and defined set of tasks and steps which describe the normal means by which a company repetitively converts embryonic ideas into saleable products or services.
- product modelling
- The entire product information modelling which describes the product completely and unambiguously. It deals with two general types of information: physical product design information represented by the design model and process information, represented by the process and data model.
- progressive levels-of-detail (lod) models
- They consist of a coarse shape representation and of a sequence of small modifications, that, when applied to the coarse representation, produce shape representations at successively finer levels of detail.
- progressive transmission
- An incremental transfer of geometry between two different sites to alleviate transmission delays due to the fact that geometry tends to be very large. This incremental transfer typically tries to capture most of the geometry, in as early as possible stages of the transmission.
- projection operator
- An operator that performs a projection. A projection P applied to x has the property that P(x) = P(P(x)), i.e. that projected points are stationary points of the projection operator. Commonly, the stationary points of a projection operator are a sub-manifold of the space they act on.

### P